Homework Help:
Probability theory and statistics

1. The problem statement, all variables and given/known data
The time (minute) that it takes for a terrain runner to get around a runway is a random variable X with the tightness function
fX = (125-x)/450 , 95≤x≤125

How big is the probability of eight different runners, whose times are independent after 100 minutes:

n=8 and from X1 to Xn, we can describe independent stochastic variables, the time when the last one came into target:
Z=max(X1....Xn)
And the time the first hit the finish line:
Y= min(X1....Xn)
Further:
Fz(t) = P(Z<t)= P(max(X1,...Xn)<t)= FX1(t)....FXn(t)

in the same way:FY(t)=1-(1-Fx1(t))...(1-FXn(t))
All in goal after 100 minutes: Z≤100P(Z<100) = [FX(100)]8 = (11/36) 8

How do I think :
I interpreted "The time everyone has scored after 100 minutes" as P (X> 100)
And tried with P(100<X<125) = 1-Fx(100) = 0.69
Then 0.698 = 0.051
I know it's wrong, but this sentence "After 100 minutes ..." made me dizzy!